![International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705
www.rsisinternational.org Page 16
Active Vibration Control of Composite Plate
Chennappa H. Korishetti 1
, Deepak S. Huddar2
1
Assistant Professor, Department of Mechanical Engineering Angadi Institute of Technology & Management,
Belagavi, Karnataka, India
2
Assistant Professor, Department of Mechanical Engineering Angadi Institute of Technology & Management,
Belagavi, Karnataka, India
Abstract- A finite element modelling of composite plate with
integrated piezoelectric layers, acting as sensor/actuator, for
active vibration control is presented in this paper. The
displacement feedback (DF) and direct velocity feedback (DVF)
controls are integrated into the FE software ANSYS to perform
closed loop analysis for vibration control. A smart laminated
composite beam with different layup configurations under free
and forced vibration condition is studied and the results shows
suppression of vibration achieved successfully in both DF and
DVF controls.
Keywords- Active Vibration, Composites, Piezoelectric, Modes,
ANSYS
I. INTRODUCTION
ibration control is an important and rapidly developing
field for lightweight flexible structures. Those structures
may get damaged or become ineffective under the undesired
vibrational loads they constantly experience. Hence, they
require effective control mechanism to attenuate the vibration
levels in order to preserve the structural integrity. The
inherent damping of these structures to suppress vibration
response is very small. Hence, active vibration control
methods are very useful to control the vibration. After the
emergence of smart materials, researchers found smarter way
of reducing the vibration that is called as active vibration
control using piezoelectric materials. Piezoelectric materials
are able to exhibit a strong coupling between the mechanical
degrees of freedom and the electrical degrees of freedom.
These materials have the unusual capability of converting
mechanical strain energy into electrical energy and vice versa.
This is the unique property which made researchers to turn
their head towards these materials. Piezoelectric materials are
preferred because of their unique coupling nature.
Investigations on active vibration control of
smart/intelligent shells with a distributed piezoelectric sensor
and actuator layer bonded on to the top and bottom surfaces of
the structures are available in a number of literatures [1]
.
Numerical investigation to analyse the free edge effect in
laminated piezoelectric plates using finite element method
was presented by J. Artel et al. [2]
. Two different cross-ply and
one angle-ply laminates have been investigated and the results
for uncoupled and coupled analysis have been compared. It
was found that the interlaminar stresses at the free edge were
significantly higher in the coupled case for cross-ply
laminates, whereas the coupling effect for the symmetric
angle-ply laminate was of lower significance. Pinto Correia et
al. [3]
developed a semi-analytical axisymmetric shell finite
element model with embedded or surface bonded
piezoelectric ring actuators or sensors for active damping
vibration control of the structure. Feedback control algorithm
was used to achieve a mechanism of active control. Based on
Kirchoff classical theory Jose M. Simoes Moita et al.[4]
presented the finite element formulation for active control of
composite structures covered with piezoelectric layers. Levent
Malgaca et al.[5]
outlined the vibration control problems which
can be directly and systematically solved using finite element
programs. They also studied the active vibration control of
forced and free vibration in laminated composite structures
with different lay-ups.
In present study, Finite element modelling of composite
beam with piezoelectric material for active vibration control is
presented. Displacement feedback (DF) and direct velocity
feedback (DVF) controls are studied for vibration control of
composite with different lay-up configurations under free and
forced vibration modes.
II. METHOD AND METHODOLOGY
The finite element method has become a powerful tool for
the numerical solution of a wide range of engineering
problems. Finite element method in general and commercial
software in particular implemented on a computer offers a
universal procedure for engineering analysis. The focus of this
work is on use of ANSYS software for simulation of
Vibration control in a piezoelectric composite beam.
A cantilever beam made of laminated Glass-epoxy
composite material bonded with piezoelectric sensor/actuator
is considered in the present work. Finite element model of the
beam developed using ANSYS software is presented. The
model is validated using benchmark. Two configurations viz.,
[0/90]s and [45/-45]s are considered for the laminates.
Vibration control of the composite beam using PZT actuator
is studied with DF and DVF control for Free vibration and
Forced vibration modes.
A. Finite Element Modelling
Finite element modelling is defined here is analyst's choice
of material models, finite elements (type, shape, and order),
meshes, constraint equations, analysis procedures, governing
differential equations and their solution methods, specific pre-
processing and post-processing options implemented in
V](https://image.slidesharecdn.com/16-22-170709024233/85/Active-Vibration-Control-of-Composite-Plate-1-320.jpg)
![International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705
www.rsisinternational.org Page 17
ANSYS for coupled field analysis. A smart cantilever beam is
considered for validation of FE model. The geometric
dimensions and material properties are given in table 1. Finite
element model of the composite beam is as shown in figure 2.
SOLID185 and SOLID5[7]
elements are considered to model
beam and actuator respectively. Modal analysis of the
composite beam is performed to obtain the natural frequencies
using the Block Lanczos solver. The obtained natural
frequencies are listed in table 2. The comparison of frequency
response with experimental study is as shown in Fig 3.
Table 1. Material and Geometric properties of smart structure
Material Properties Geometric properties
Glass-Epoxy Composite Piezoelectric material[5]
(BM532)
Piezoelectric material[6]
(PZT-4)
Beam Actuator
ρ =1830 kg/m3
Elastic constants (N/m2
)
Ex=40.51 x 109
Ey=13.96 x 109
Ez=13.96 x 109
Gxy=3.1 x 109
Gyz=1.55 x 109
Gxz=3.1 x 109
νxy= 0.22
νyz= 0.11
νxz= 0.22
ρ = 7350 kg/m3
Elastic stiffness matrix (N/m2
)
C11 =12.6 x 1010
C12 =7.95 x 1010
C13 =8.41 x 1010
C33 =11.7 x 1010
C44=2.33 x 1010
Piezoelectric constants (C/m2
)
e31 = e32 = 6.5
e24 = e15 = 17
e33 = 23.3
Dielectric Constants (F/m)
ɛ11=ɛ22=1.503x10-8
ɛ33 = 1.3 10-8
ρ = 7500 kg/m3
Elastic stiffness matrix (N/m2
)
C11 =13.9 x 1010
C12 =7.78 x 1010
C13 =7.43 x 1010
C33 =11.53 x 1010
C44 =2.56 x 1010
Piezoelectric constants (C/m2
)
e31 = e32 = 6.5
e24 = e15 = 17
e33 = 23.3
Dielectric Constants (F/m)
ɛ11=ɛ22=1.503x10-8
ɛ33 = 1.3 10-8
L = 345 mm
b = 20 mm
t1 = 0.85 mm
t2=0.02125mm
B = 25 mm
b = 20 mm
t3 = 0.5mm
da = 5mm
Fig. 1 Smart Cantilever Beam
Fig. 2 FE Model of smart beam and lay-ups
Table 2 Comparison of natural frequencies
Mode
Natural frequencies (Hz)
Ref [5]
Present study
1 5.9678 5.7900
2 36.5700 36.0800
3 87.5280 87.3210
(b)
(a)](https://image.slidesharecdn.com/16-22-170709024233/85/Active-Vibration-Control-of-Composite-Plate-2-320.jpg)
![International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705
www.rsisinternational.org Page 18
Fig. 3 Comparison of frequency response (a)Present results (b) Target
results [5]
The obtained natural frequencies are in agreement with
experimental results. It is observed from the results (figure 3
and table 2) that the layered element (SOLID185) and
SOLID5 element can be used to model laminated composite
beam with piezoelectric layers.
B. Coupled Field Analysis
The coupled field analysis is a combination of analyses
from different engineering disciplines (physics fields) that
interact to solve a global engineering problem. Hence, we
often refer to a coupled field analysis as a multiphysics
analysis. There are different types of coupled field analysis,
for piezoelectric analysis ANSYS uses direct coupled field
analysis. The direct method usually involves just one analysis
that uses a coupled-field element type containing all necessary
degrees of freedom. Coupling is handled by calculating
element matrices or element load vectors that contain all
necessary terms.
C.Piezoelectric Analysis
Piezoelectric analysis is the coupling of structural and
electric fields. Applying a voltage to a piezoelectric material
creates a displacement, and vibrating a piezoelectric material
generates voltage. Possible piezoelectric analysis types,
available in ANSYS Multiphysics or ANSYS Mechanical
products are static, modal, pre-stressed modal, harmonic, pre-
stressed harmonic, and transient. Some important points to
remember are:
For modal analysis, Block Lanczos is the
recommended solver.
For static, full harmonic and full transient analysis the
sparse matrix (SPARSE) solver or the Jacobi
Conjugate Gradient (JCG) solver is preferred. The
sparse solver is the default for static and full transient
analyses.
For transient analyses, specify ALPHA= 0.25, DELTA
= 0.5, and THETA=0.5 on the TINTP command (Main
Menu> Preprocessor> Loads> Time/Frequency> Time
Integration).
D.Governing Matrix Equations
The electromechanical constitutive equation for linear
material behaviour are
{T} = [c]{S} ‒ [e]{E}
{D} = [e]{S} + [ɛ]{E}
After the application of the variational principle and finite
element discretization, the equations of motion for coupled
piezoelectric is,
The explanation of sub- matrices is referred in [7]
.
E. Solution Method
Several methods for solving the simultaneous equations of
the system are available in the ANSYS program: Sparse direct
solution, Preconditioned Conjugate Gradient (PCG) solution,
Jacobi Conjugate Gradient (JCG) solution, Incomplete
Cholesky Conjugate Gradient (ICCG) solution, automatic
iterative solver option (ITER) and frontal direct solution.
The sparse direct solver is based on a direct elimination of
equations, as opposed to iterative solvers, where the solution
is obtained through an iterative process that successively
refines an initial guess to a solution that is within an
acceptable tolerance of the exact solution.
To perform closed loop analysis displacement feedback
(DF) and direct velocity feedback (DVF) controls are studied.
The block diagrams of DF and DVF controls are as shown in
figure 4 and 5 respectively.
Fig. 4 Block diagram of DF control
Fig. 5 Block diagram of DVF control
In DF control, the reference value is taken as zero to cancel
the vibration and the displacement value from sensor is
compared with reference value to determine the error value.
The actuation voltage is calculated by multiplying error value
(1)
(2)](https://image.slidesharecdn.com/16-22-170709024233/85/Active-Vibration-Control-of-Composite-Plate-3-320.jpg)
![International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705
www.rsisinternational.org Page 19
with amplification factors. The actuation voltage is applied to
actuator, the process continues until steady state response is
reached. In DVF control, velocity feedback is calculated by
dividing displacement value to dt. The error value is
multiplied by Ks and Kv to find the actuation voltage. The
actuation voltage is applied to actuator, the process continues
until steady state response is reached.
III. ACTIVE VIBRATION CONTROL OF COMPOSITE
BEAM
On validation of finite element model of composite
structures, the method is used for active vibration control of
cantilever beam under free and forced vibration.
A smart laminated composite cantilever with [0/90]s and
[45/-45]s ply orientation is considered for active vibration
control as shown in the figure 2. The actuator bonded to the
beam is of PZT-4 material. The material and geometric
properties are given in table 1. In the analysis, nodes on upper
surface of the actuator are coupled to apply actuator voltage
uniformly on the nodes.
Modal analysis of the beam is performed to obtain the first
mode frequency and the time step (dt). Time step dt is given
by 1/20f1, where f1 is first natural frequency. For [0/90]s and
[45/45s ply orientation the first mode frequencies are 5.79002
Hz and 3.1802 Hz respectively and the time steps are 0.0084
sec and 0.0152 sec respectively.
Transient analysis is performed to plot time history of tip
deflection. Rayleigh damping coefficients used for the
analysis are α = 0.00117, β = 0.000585 for [0/90]s lay-up and
α = 0.00187, β = 0.000935 for [45/-45]s lay-up[6]
. Newmark's
method is used for time integration with a time step of dt.
Displacement Feedback and Direct Velocity Feedback control
gain theories are used for active vibration control. The power
amplification value Kv is taken as 30 and sensor amplification
value Ks is 250 for displacement sensor.
A. Free Vibration
Figure 6 shows the boundary condition applied before
commencement of closed loop analysis. A tip displacement of
0.02m is applied in z-direction for duration dt. DF and DVF
controls are studied for vibration control.
Fig. 6 FE model with boundary conditions (free vibration)
Fig. 7 Time response plots for different gain values under free vibration for
[0/90]s: (a) and (c) DF control, (b) and (d) DVF control
(a)
(b)
(c)
(d)
[0/90]s
[0/90]s
[0/90]s
[0/90]s](https://image.slidesharecdn.com/16-22-170709024233/85/Active-Vibration-Control-of-Composite-Plate-4-320.jpg)
![International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705
www.rsisinternational.org Page 20
Fig. 8 Time response plots for different gain values under free vibration for
[45/-45]s: (a) and (c) DF control, (b) and (d) DVF control
Figure 7 and 8 shows uncontrolled and controlled time
responses and actuation voltage responses of DF and DVF
controls for [0/90]s and [45/-45]s lay-ups respectively. It is
observed from results that as the control gain increases the tip
deflection decreases and the vibration is successfully
controlled in both controls and it can be seen that the time
taken to reach steady state is less in DVF control than DF
control. Figure 9 shows the comparison of actuation voltage
with controller gains.
Fig. 9 Comparison of actuation voltage with gain values
B. Forced Vibration
To investigate the response under forced vibration, a step
force in z-direction is applied at the tip of beam. The
magnitude of step force is chosen to have 0.02 m static tip
deflection. The magnitude of forces are 0.0713N and 0.0210N
for [0/90]s and [45/-45]s respectively. FE model with boundary
conditions and loads is shown in figure 10.
Fig. 10 FE model with boundary conditions (forced vibration)
(d)
(c)
(b)
(a)
[45/-45]s
[45/-45]s
[45/-45]s
[45/-45]s](https://image.slidesharecdn.com/16-22-170709024233/85/Active-Vibration-Control-of-Composite-Plate-5-320.jpg)
![International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705
www.rsisinternational.org Page 21
Fig. 11 Time response plots for different gain values under forced vibration
using DF control (a) [0/90]s, (b) [45/-45]s
Fig. 12 Time response plots for different gain values under forced vibration
using DVF control (a) [0/90]s, (b) [45/-45]s
Figures 11 and 12 show uncontrolled and controlled time
responses of forced vibration. It is observed from results that
as the control gain increases the tip deflection decreases and
the time taken to reach steady state is less in DVF control than
DF control.
IV.SUMMARY
Piezoelectric materials have major role in active vibration
control. Piezoelectric materials are preferred for active
vibration control because of their coupling nature. These
materials are inexpensive, lightweight and easily bonded on to
the surface and embedded into the structures. ANSYS software
provides a mean for FE modelling of smart structures, coupled
field analysis and closed loop control actions can be simulated
by integrating control laws into the ANSYS.
In this study, Active vibration controls of composite
structures with piezoelectric material under free and forced
vibrations are studied. The responses of structure using
different control laws have been demonstrated. It is observed
that the time taken to reach steady state using DVF control is
relatively smaller than that of DF control.
REFERRENCES
[1]. V. Balamurugan and S. Narayanan, Shell finite element for smart
piezoelectric composite plate/shell structures and its application to
study of active vibration control, Finite elements in Analysis and
Design, vol. 37, 2001 pp.713-738.
[2]. J. Artel and W. Becker, Coupled and uncoupled analyses of
piezoelectric free-edge effect in laminated plates, Composite
Structures, vol. 69, 2005, pp.329-335.
[3]. I. F. Pinto Correia, Cristovao M. Moto Soares, Carlos A. Mota
Soares, and J. Herskovits, Active control of axisymmetric shells
with piezoelectric layers: a mixed laminated theory with a higher
order field, Computers and Structures, vol. 80, 2002, pp.2265-
2275.
[4]. Jose M. Simoes Moita, Isidoro F. P. Correia, Cristovao M. Moto
Soares, and Carlos A. Mota Soares, Active control of adaptive
laminated structures with bonded piezoelectric sensors and
actuators, Computers and Structures, vol. 82, 2004, pp.1349-1358.
[5]. Levent Malgaca, Integration of active vibration control methods
with finite element models of smart laminated composite structures,
Composite Structures, vol. 92, 2010, pp.1651-1663.
[6]. H. Boudaoud, E. M. Daya, S. Belouettar, L. Duigou and M. potier-
Ferry, Damping analysis of beams submitted to passive and active
control, Engineering Structures, vol. 31, 2009pp. 322-331.
[7]. ANSYS User Manual (release 14.0).
AUTHOR'S PROFILE
CHENNAPPA H. KORISHETTI1
Has received his Mastеr
of Tеchnology in Design Engineеring from DSCE, Bengaluru
in the yеar 2013, his Bachelor of Engineering degree in
Mechanical Engineering from KLE College of Engineering
and Technology, Belagavi in the year 2011. At present
working as an Assistant Professor in Angadi Institute of
Technology and Management. His area of interests is
Mechanical Vibrations, Composite Materials, FEM, Machine
Design.
(a)
(b)
(a)
(b)
[45/-45]s
[45/-45]s
[0/90]s
[0/90]s](https://image.slidesharecdn.com/16-22-170709024233/85/Active-Vibration-Control-of-Composite-Plate-6-320.jpg)
Active Vibration Control of Composite Plate
- 1. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 16 Active Vibration Control of Composite Plate Chennappa H. Korishetti 1 , Deepak S. Huddar2 1 Assistant Professor, Department of Mechanical Engineering Angadi Institute of Technology & Management, Belagavi, Karnataka, India 2 Assistant Professor, Department of Mechanical Engineering Angadi Institute of Technology & Management, Belagavi, Karnataka, India Abstract- A finite element modelling of composite plate with integrated piezoelectric layers, acting as sensor/actuator, for active vibration control is presented in this paper. The displacement feedback (DF) and direct velocity feedback (DVF) controls are integrated into the FE software ANSYS to perform closed loop analysis for vibration control. A smart laminated composite beam with different layup configurations under free and forced vibration condition is studied and the results shows suppression of vibration achieved successfully in both DF and DVF controls. Keywords- Active Vibration, Composites, Piezoelectric, Modes, ANSYS I. INTRODUCTION ibration control is an important and rapidly developing field for lightweight flexible structures. Those structures may get damaged or become ineffective under the undesired vibrational loads they constantly experience. Hence, they require effective control mechanism to attenuate the vibration levels in order to preserve the structural integrity. The inherent damping of these structures to suppress vibration response is very small. Hence, active vibration control methods are very useful to control the vibration. After the emergence of smart materials, researchers found smarter way of reducing the vibration that is called as active vibration control using piezoelectric materials. Piezoelectric materials are able to exhibit a strong coupling between the mechanical degrees of freedom and the electrical degrees of freedom. These materials have the unusual capability of converting mechanical strain energy into electrical energy and vice versa. This is the unique property which made researchers to turn their head towards these materials. Piezoelectric materials are preferred because of their unique coupling nature. Investigations on active vibration control of smart/intelligent shells with a distributed piezoelectric sensor and actuator layer bonded on to the top and bottom surfaces of the structures are available in a number of literatures [1] . Numerical investigation to analyse the free edge effect in laminated piezoelectric plates using finite element method was presented by J. Artel et al. [2] . Two different cross-ply and one angle-ply laminates have been investigated and the results for uncoupled and coupled analysis have been compared. It was found that the interlaminar stresses at the free edge were significantly higher in the coupled case for cross-ply laminates, whereas the coupling effect for the symmetric angle-ply laminate was of lower significance. Pinto Correia et al. [3] developed a semi-analytical axisymmetric shell finite element model with embedded or surface bonded piezoelectric ring actuators or sensors for active damping vibration control of the structure. Feedback control algorithm was used to achieve a mechanism of active control. Based on Kirchoff classical theory Jose M. Simoes Moita et al.[4] presented the finite element formulation for active control of composite structures covered with piezoelectric layers. Levent Malgaca et al.[5] outlined the vibration control problems which can be directly and systematically solved using finite element programs. They also studied the active vibration control of forced and free vibration in laminated composite structures with different lay-ups. In present study, Finite element modelling of composite beam with piezoelectric material for active vibration control is presented. Displacement feedback (DF) and direct velocity feedback (DVF) controls are studied for vibration control of composite with different lay-up configurations under free and forced vibration modes. II. METHOD AND METHODOLOGY The finite element method has become a powerful tool for the numerical solution of a wide range of engineering problems. Finite element method in general and commercial software in particular implemented on a computer offers a universal procedure for engineering analysis. The focus of this work is on use of ANSYS software for simulation of Vibration control in a piezoelectric composite beam. A cantilever beam made of laminated Glass-epoxy composite material bonded with piezoelectric sensor/actuator is considered in the present work. Finite element model of the beam developed using ANSYS software is presented. The model is validated using benchmark. Two configurations viz., [0/90]s and [45/-45]s are considered for the laminates. Vibration control of the composite beam using PZT actuator is studied with DF and DVF control for Free vibration and Forced vibration modes. A. Finite Element Modelling Finite element modelling is defined here is analyst's choice of material models, finite elements (type, shape, and order), meshes, constraint equations, analysis procedures, governing differential equations and their solution methods, specific pre- processing and post-processing options implemented in V
- 2. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 17 ANSYS for coupled field analysis. A smart cantilever beam is considered for validation of FE model. The geometric dimensions and material properties are given in table 1. Finite element model of the composite beam is as shown in figure 2. SOLID185 and SOLID5[7] elements are considered to model beam and actuator respectively. Modal analysis of the composite beam is performed to obtain the natural frequencies using the Block Lanczos solver. The obtained natural frequencies are listed in table 2. The comparison of frequency response with experimental study is as shown in Fig 3. Table 1. Material and Geometric properties of smart structure Material Properties Geometric properties Glass-Epoxy Composite Piezoelectric material[5] (BM532) Piezoelectric material[6] (PZT-4) Beam Actuator ρ =1830 kg/m3 Elastic constants (N/m2 ) Ex=40.51 x 109 Ey=13.96 x 109 Ez=13.96 x 109 Gxy=3.1 x 109 Gyz=1.55 x 109 Gxz=3.1 x 109 νxy= 0.22 νyz= 0.11 νxz= 0.22 ρ = 7350 kg/m3 Elastic stiffness matrix (N/m2 ) C11 =12.6 x 1010 C12 =7.95 x 1010 C13 =8.41 x 1010 C33 =11.7 x 1010 C44=2.33 x 1010 Piezoelectric constants (C/m2 ) e31 = e32 = 6.5 e24 = e15 = 17 e33 = 23.3 Dielectric Constants (F/m) ɛ11=ɛ22=1.503x10-8 ɛ33 = 1.3 10-8 ρ = 7500 kg/m3 Elastic stiffness matrix (N/m2 ) C11 =13.9 x 1010 C12 =7.78 x 1010 C13 =7.43 x 1010 C33 =11.53 x 1010 C44 =2.56 x 1010 Piezoelectric constants (C/m2 ) e31 = e32 = 6.5 e24 = e15 = 17 e33 = 23.3 Dielectric Constants (F/m) ɛ11=ɛ22=1.503x10-8 ɛ33 = 1.3 10-8 L = 345 mm b = 20 mm t1 = 0.85 mm t2=0.02125mm B = 25 mm b = 20 mm t3 = 0.5mm da = 5mm Fig. 1 Smart Cantilever Beam Fig. 2 FE Model of smart beam and lay-ups Table 2 Comparison of natural frequencies Mode Natural frequencies (Hz) Ref [5] Present study 1 5.9678 5.7900 2 36.5700 36.0800 3 87.5280 87.3210 (b) (a)
- 3. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 18 Fig. 3 Comparison of frequency response (a)Present results (b) Target results [5] The obtained natural frequencies are in agreement with experimental results. It is observed from the results (figure 3 and table 2) that the layered element (SOLID185) and SOLID5 element can be used to model laminated composite beam with piezoelectric layers. B. Coupled Field Analysis The coupled field analysis is a combination of analyses from different engineering disciplines (physics fields) that interact to solve a global engineering problem. Hence, we often refer to a coupled field analysis as a multiphysics analysis. There are different types of coupled field analysis, for piezoelectric analysis ANSYS uses direct coupled field analysis. The direct method usually involves just one analysis that uses a coupled-field element type containing all necessary degrees of freedom. Coupling is handled by calculating element matrices or element load vectors that contain all necessary terms. C.Piezoelectric Analysis Piezoelectric analysis is the coupling of structural and electric fields. Applying a voltage to a piezoelectric material creates a displacement, and vibrating a piezoelectric material generates voltage. Possible piezoelectric analysis types, available in ANSYS Multiphysics or ANSYS Mechanical products are static, modal, pre-stressed modal, harmonic, pre- stressed harmonic, and transient. Some important points to remember are: For modal analysis, Block Lanczos is the recommended solver. For static, full harmonic and full transient analysis the sparse matrix (SPARSE) solver or the Jacobi Conjugate Gradient (JCG) solver is preferred. The sparse solver is the default for static and full transient analyses. For transient analyses, specify ALPHA= 0.25, DELTA = 0.5, and THETA=0.5 on the TINTP command (Main Menu> Preprocessor> Loads> Time/Frequency> Time Integration). D.Governing Matrix Equations The electromechanical constitutive equation for linear material behaviour are {T} = [c]{S} ‒ [e]{E} {D} = [e]{S} + [ɛ]{E} After the application of the variational principle and finite element discretization, the equations of motion for coupled piezoelectric is, The explanation of sub- matrices is referred in [7] . E. Solution Method Several methods for solving the simultaneous equations of the system are available in the ANSYS program: Sparse direct solution, Preconditioned Conjugate Gradient (PCG) solution, Jacobi Conjugate Gradient (JCG) solution, Incomplete Cholesky Conjugate Gradient (ICCG) solution, automatic iterative solver option (ITER) and frontal direct solution. The sparse direct solver is based on a direct elimination of equations, as opposed to iterative solvers, where the solution is obtained through an iterative process that successively refines an initial guess to a solution that is within an acceptable tolerance of the exact solution. To perform closed loop analysis displacement feedback (DF) and direct velocity feedback (DVF) controls are studied. The block diagrams of DF and DVF controls are as shown in figure 4 and 5 respectively. Fig. 4 Block diagram of DF control Fig. 5 Block diagram of DVF control In DF control, the reference value is taken as zero to cancel the vibration and the displacement value from sensor is compared with reference value to determine the error value. The actuation voltage is calculated by multiplying error value (1) (2)
- 4. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 19 with amplification factors. The actuation voltage is applied to actuator, the process continues until steady state response is reached. In DVF control, velocity feedback is calculated by dividing displacement value to dt. The error value is multiplied by Ks and Kv to find the actuation voltage. The actuation voltage is applied to actuator, the process continues until steady state response is reached. III. ACTIVE VIBRATION CONTROL OF COMPOSITE BEAM On validation of finite element model of composite structures, the method is used for active vibration control of cantilever beam under free and forced vibration. A smart laminated composite cantilever with [0/90]s and [45/-45]s ply orientation is considered for active vibration control as shown in the figure 2. The actuator bonded to the beam is of PZT-4 material. The material and geometric properties are given in table 1. In the analysis, nodes on upper surface of the actuator are coupled to apply actuator voltage uniformly on the nodes. Modal analysis of the beam is performed to obtain the first mode frequency and the time step (dt). Time step dt is given by 1/20f1, where f1 is first natural frequency. For [0/90]s and [45/45s ply orientation the first mode frequencies are 5.79002 Hz and 3.1802 Hz respectively and the time steps are 0.0084 sec and 0.0152 sec respectively. Transient analysis is performed to plot time history of tip deflection. Rayleigh damping coefficients used for the analysis are α = 0.00117, β = 0.000585 for [0/90]s lay-up and α = 0.00187, β = 0.000935 for [45/-45]s lay-up[6] . Newmark's method is used for time integration with a time step of dt. Displacement Feedback and Direct Velocity Feedback control gain theories are used for active vibration control. The power amplification value Kv is taken as 30 and sensor amplification value Ks is 250 for displacement sensor. A. Free Vibration Figure 6 shows the boundary condition applied before commencement of closed loop analysis. A tip displacement of 0.02m is applied in z-direction for duration dt. DF and DVF controls are studied for vibration control. Fig. 6 FE model with boundary conditions (free vibration) Fig. 7 Time response plots for different gain values under free vibration for [0/90]s: (a) and (c) DF control, (b) and (d) DVF control (a) (b) (c) (d) [0/90]s [0/90]s [0/90]s [0/90]s
- 5. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 20 Fig. 8 Time response plots for different gain values under free vibration for [45/-45]s: (a) and (c) DF control, (b) and (d) DVF control Figure 7 and 8 shows uncontrolled and controlled time responses and actuation voltage responses of DF and DVF controls for [0/90]s and [45/-45]s lay-ups respectively. It is observed from results that as the control gain increases the tip deflection decreases and the vibration is successfully controlled in both controls and it can be seen that the time taken to reach steady state is less in DVF control than DF control. Figure 9 shows the comparison of actuation voltage with controller gains. Fig. 9 Comparison of actuation voltage with gain values B. Forced Vibration To investigate the response under forced vibration, a step force in z-direction is applied at the tip of beam. The magnitude of step force is chosen to have 0.02 m static tip deflection. The magnitude of forces are 0.0713N and 0.0210N for [0/90]s and [45/-45]s respectively. FE model with boundary conditions and loads is shown in figure 10. Fig. 10 FE model with boundary conditions (forced vibration) (d) (c) (b) (a) [45/-45]s [45/-45]s [45/-45]s [45/-45]s
- 6. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 21 Fig. 11 Time response plots for different gain values under forced vibration using DF control (a) [0/90]s, (b) [45/-45]s Fig. 12 Time response plots for different gain values under forced vibration using DVF control (a) [0/90]s, (b) [45/-45]s Figures 11 and 12 show uncontrolled and controlled time responses of forced vibration. It is observed from results that as the control gain increases the tip deflection decreases and the time taken to reach steady state is less in DVF control than DF control. IV.SUMMARY Piezoelectric materials have major role in active vibration control. Piezoelectric materials are preferred for active vibration control because of their coupling nature. These materials are inexpensive, lightweight and easily bonded on to the surface and embedded into the structures. ANSYS software provides a mean for FE modelling of smart structures, coupled field analysis and closed loop control actions can be simulated by integrating control laws into the ANSYS. In this study, Active vibration controls of composite structures with piezoelectric material under free and forced vibrations are studied. The responses of structure using different control laws have been demonstrated. It is observed that the time taken to reach steady state using DVF control is relatively smaller than that of DF control. REFERRENCES [1]. V. Balamurugan and S. Narayanan, Shell finite element for smart piezoelectric composite plate/shell structures and its application to study of active vibration control, Finite elements in Analysis and Design, vol. 37, 2001 pp.713-738. [2]. J. Artel and W. Becker, Coupled and uncoupled analyses of piezoelectric free-edge effect in laminated plates, Composite Structures, vol. 69, 2005, pp.329-335. [3]. I. F. Pinto Correia, Cristovao M. Moto Soares, Carlos A. Mota Soares, and J. Herskovits, Active control of axisymmetric shells with piezoelectric layers: a mixed laminated theory with a higher order field, Computers and Structures, vol. 80, 2002, pp.2265- 2275. [4]. Jose M. Simoes Moita, Isidoro F. P. Correia, Cristovao M. Moto Soares, and Carlos A. Mota Soares, Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators, Computers and Structures, vol. 82, 2004, pp.1349-1358. [5]. Levent Malgaca, Integration of active vibration control methods with finite element models of smart laminated composite structures, Composite Structures, vol. 92, 2010, pp.1651-1663. [6]. H. Boudaoud, E. M. Daya, S. Belouettar, L. Duigou and M. potier- Ferry, Damping analysis of beams submitted to passive and active control, Engineering Structures, vol. 31, 2009pp. 322-331. [7]. ANSYS User Manual (release 14.0). AUTHOR'S PROFILE CHENNAPPA H. KORISHETTI1 Has received his Mastеr of Tеchnology in Design Engineеring from DSCE, Bengaluru in the yеar 2013, his Bachelor of Engineering degree in Mechanical Engineering from KLE College of Engineering and Technology, Belagavi in the year 2011. At present working as an Assistant Professor in Angadi Institute of Technology and Management. His area of interests is Mechanical Vibrations, Composite Materials, FEM, Machine Design. (a) (b) (a) (b) [45/-45]s [45/-45]s [0/90]s [0/90]s
- 7. International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue VIS, June 2017 | ISSN 2321–2705 www.rsisinternational.org Page 22 DEEPAK S. HUDDAR2 Has received his Master of Technology in Design Engineering from KLE College of Engineering and Technology, Belagavi in the year 2014, his Bachelor of Engineering degree in Mechanical Engineering from Agadi Engineering College, Laxmeshwar in the year 2010. At present working as an Assistant Professor in Angadi Institute of Technology and Management. His area of interests is Mechanical Vibrations, Composite Materials, FEM, Fracture Mechanics.